AEPA Mathematics (NT304) study plan
AEPA Mathematics (NT304) · Give each week a clear focus.
8 weeks · About 6 hours per week
Mathematical Processes and Number Sense
Classify real numbers into subsets and justify each classification with a definition
Convert fluently among fractions, decimals, and percents, including repeating decimals
Apply order-of-operations rules to multi-step expressions without a calculator
Compute with integer exponents and simplify radical expressions
Your checkpoint
A 25-item worked problem set on number systems, operations, and exponents, scored with corrections written for every miss
Mathematical Processes and Number Sense
Solve multi-step ratio, proportion, and percent problems including percent change and tax/discount
Model and solve real-world problems involving rational numbers and unit rates
Explain and apply divisibility rules, GCF, and LCM to simplify and combine expressions
Identify and correct student-style errors in number-sense reasoning
Your checkpoint
A one-page error-analysis log of 10 intentionally flawed solutions, each with the misconception named and a corrected solution
Patterns, Algebra, and Functions
Extend and describe arithmetic and geometric patterns using both recursive and explicit rules
Translate among verbal, tabular, graphical, and symbolic representations of a function
Evaluate and interpret function notation across linear and quadratic contexts
Distinguish functions from non-functions using multiple representations
Your checkpoint
A representation-matching portfolio of 12 functions shown in all four forms, verified for consistency
Patterns, Algebra, and Functions & Mathematical Processes and Number Sense
Solve and graph linear equations and inequalities, including compound and absolute-value cases
Derive slope and intercepts from tables, graphs, and two points, and interpret them in context
Build systems of two linear equations and solve them by graphing, substitution, and elimination
Recognize and extend exponential growth and decay patterns from data
Your checkpoint
A timed 20-question mixed algebra and number-sense quiz completed in 40 minutes with at least 85% accuracy
Patterns, Algebra, and Functions
Factor and expand polynomial expressions and connect the factors to graph intercepts
Solve quadratic equations by factoring, completing the square, and the quadratic formula
Interpret the discriminant and the vertex in applied maximum/minimum problems
Simplify rational expressions and identify restricted domain values
Your checkpoint
A written solution set for 15 quadratic and polynomial problems that shows the method choice and a graph sketch for each
Measurement and Geometry
Convert within and between metric and customary measurement systems with correct unit cancellation
Compute perimeter, area, surface area, and volume for composite figures
Apply the Pythagorean theorem and distance formula to solve geometric problems
Classify polygons and solids by their defining properties and justify each classification
Your checkpoint
A two-page composite-figure reference sheet with four original worked problems, each showing dimensional analysis and units
Measurement and Geometry & Statistics, Probability, and Discrete Mathematics
Apply angle relationships, similarity, and congruence to find unknown measures
Perform and describe transformations on the coordinate plane, including dilations and scale factors
Compute mean, median, mode, range, and standard deviation and interpret what each reveals
Construct and read box plots, histograms, and scatterplots to describe data distributions
Your checkpoint
A geometry-and-data mini-project: one scaled figure design with a written analysis plus a statistical summary of a 20-value data set you construct
Statistics, Probability, and Discrete Mathematics & Mathematical Processes and Number Sense & Patterns, Algebra, and Functions & Measurement and Geometry
Compute and interpret experimental versus theoretical probability, including compound and conditional events
Apply counting principles, permutations, and combinations to solve arrangement problems
Model discrete situations with sequences, series, and simple networks or matrices
Diagnose and correct your own recurring errors across all four domains under timed conditions
Your checkpoint
A full-length 60-question timed practice exam with a scored error log grouping misses by domain and a prioritized final-review list
Milestones
Week 2: Score at least 80% on a self-made 20-question number-sense set and explain every correction aloud without notes
Week 4: Complete the 20-question mixed quiz in 40 minutes at 85% or better, with no more than two algebra errors
Week 6: Solve all four composite-figure problems with correct units and dimensional analysis on the first attempt
Week 8: Score at least 80% overall on the 60-question practice exam with no single domain below 70%